Expected Returns and Expected Growth in Rents of Commercial Real Estate


 Scarlett Miles
 3 years ago
 Views:
Transcription
1 Expected Returns and Expected Growth in Rents of Commercial Real Estate Alberto Plazzi Walter Torous Rossen Valkanov This Version: January 2010 Abstract Commercial real estate expected returns and expected rent growth rates are timevarying. Relying on transactions data from a crosssection of U.S. metropolitan areas, we find that up to 30% of the variability of realized returns to commercial real estate can be accounted for by expected return variability, while expected rent growth rate variability explains up to 45% of the variability of realized rent growth rates. The cap rate, that is, the rentprice ratio in commercial real estate, captures fluctuations in expected returns for apartments, retail, as well as industrial properties. For offices, by contrast, cap rates do not forecast (insample) returns even though expected returns on offices are also timevarying. As implied by the present value relation, cap rates marginally forecast office rent growth but not rent growth of apartments, retail and industrial properties. We link these differences in insample predictability to differences in the stochastic properties of the underlying commercial real estate data generating processes. Also, rent growth predictability is mostly observed in locations characterized by higher population density and stringent land use restrictions. The opposite is true for return predictability. The dynamic portfolio implications of timevarying commercial real estate returns are also explored in the context of a portfolio manager investing in the aggregate stock market, Treasury bills as well as commercial real estate. We thank Andrea Berardi, Markus Brunnermeier (AFA discussant), Christopher Downing, Erasmo Giambona (EFA discussant), Harrison Hong, Andrey Pavlov, Antonio Rubia, Stephen Schaefer and seminar participants at the following conferences for useful comments: the AFA 2007 Meeting, the AREUEA, the XXXIV EFA Meeting, the XXXVI EWGFM, the FMA European meeting, the SAET meeting in Vigo, and the SAFE center at the University of Verona. We are especially grateful to an anonymous referee and the Editor, Matthew Spiegel, for many suggestions that have greatly improved the paper. All remaining errors are our own. The Anderson School at UCLA and SAFE Center University of Verona, 110 Westwood Plaza, Los Angeles, CA , phone: (310) , fax: (310) , The Anderson School at UCLA, 110 Westwood Plaza, Los Angeles, CA , phone: (310) , fax: (310) , Corresponding author. Rady School at UCSD, Pepper Canyon Hall, 9500 Gilman Drive, MC 0093, La Jolla, CA 92093, phone: (858) , fax: (858) , The latest draft is available at:
2 1 Introduction U.S. commercial real estate prices fluctuate considerably, both crosssectionally as well as over time. For example, the return to apartment buildings during the last quarter of 1994 ranged from 21.4 percent in Dallas, Texas to 8.5 percent in Portland, Oregon. Eight years later, during the last quarter of 2002, the returns to apartments in Dallas and Portland were 1.2 percent and 4.4 percent, respectively. Other types of commercial real estate, such as retail, industrial, and office properties, have experienced even larger return fluctuations. Understanding what drives these fluctuations is an important research question as commercial real estate represents a substantial fraction of total U.S. wealth. For example, Standard and Poor s estimates the value in 2007 of all U.S. commercial real estate to be about $5.3 trillion, about one fifth of the stock market s value. From an asset pricing perspective, the price of a commercial property, be it an office building, apartment, retail or industrial space, equals the present value of its future rents. This fundamental present value relation implies that observed fluctuations in commercial real estate prices should reflect variation in future rents, or in future discount rates, or both. The possibility of timevarying discount rates and rent growth rates should be explicitly considered in the valuation of commercial real estate as it is often conjectured that both fluctuate with the prevailing state of the economy. Case (2000), for example, points out the vulnerability of commercial real estate values to changes in economic conditions by describing recent boomandbust cycles in that market. He provides a simple example of cyclical fluctuations in expected returns and rent growth rates that give rise to sizable variation in commercial real estate values. Case, Goetzmann, and Rouwenhorst (2000) make a similar point using international data and conclude that commercial real estate is a bet on fundamental economic variables. Despite these and other studies, little is known about the dynamics of commercial real estate returns and rent growth rates. In this paper, we investigate whether expected returns and expected growth in rents of commercial real estate are timevarying by relying on a version of Campbell and Shiller s (1988b) dynamic Gordon model. An implication of this model is that the cap rate, defined as the ratio between a property s rent and its price, should reflect fluctuations in expected returns, or in rent growth rates, or both. The cap rate is a standard measure of commercial real estate valuation and corresponds to a common stock s dividendprice ratio where the property s rent plays the role of the dividend. By way of example, suppose that the cap rate for apartment buildings in Portland is higher than the cap rate of similar properties in Dallas. The dynamic Gordon model implies that either future discount rates in Portland will be higher than those expected in Dallas, or that future rents in Portland are expected to grow at a slower rate than in Dallas, or both. Commercial real estate offers a number of advantages over common stock when investigating the dynamics of expected returns and the growth in cash payouts. For example, it is often argued 1
3 that common stock dividends do not accurately reflect the changing investment opportunities confronting a firm. Dividends are paid at the discretion of the firm s management and there is extensive evidence that they are either actively smoothed, the product of managers catering to particular clienteles, or the result of management s reaction to perceived mispricing (Shefrin and Statman (1984), Stein (1996), and Baker and Wurgler (2004)). By contrast, rents on commercial properties are not discretionary and are paid by tenants as opposed to property managers. Furthermore, commercial rents are particularly sensitive to prevailing economic conditions such as employment and growth in industrial production (DiPasquale and Wheaton (1996)). In conducting our empirical analysis, we rely on a novel data set summarizing commercial real estate transactions across fiftythree U.S. metropolitan areas reported at a quarterly frequency over a sample period extending from the second quarter of 1994 to the first quarter of For a subset of twentyone of these areas, we also have biannual observations beginning in the last quarter of These data are available for a variety of property types including offices, apartments, as well as retail and industrial properties. The transactions nature of our commercial real estate data differentiates it from the appraisal data typically relied upon in other studies. For example, unlike the serially correlated returns and rent growth rates characterizing appraisal data (Case and Shiller (1989, 1990)), returns and rent growth rates in our data are not serially correlated beyond a yearly horizon. We find that higher cap rates predict higher future returns of apartment buildings as well as retail and industrial properties. Cap rates, however, do not predict the future returns of office buildings. For apartments, retail, and industrial properties, the predictability of returns is robust to controlling for crosssectional differences using variables that capture regional variation in demographic, geographic, and various economic factors. In terms of the economic significance of this relation, we find that a one percent increase in cap rates leads to an increase of up to four percent in the prices of these properties. This large effect is due to the persistence of the fluctuations in expected returns and is similar in magnitude to that documented for common stock (Cochrane (2008)). The evidence of return predictability is primarily drawn from locations characterized by lower population density and less land use restrictions. By contrast, we do not find reliable evidence that cap rate fluctuations are associated with future movements in rent growth rates. Only for offices do we find some evidence of higher cap rates predicting lower future rent growth rates and then only at long horizons. Also, rent growth predictability is more likely to be observed in locations characterized by higher population density and stricter land use restrictions. These findings, however, should only be interpreted as insample evidence because our estimation procedure relies on data drawn from the entire sample period. Therefore, our results are not predictive in the sense that an investor in realtime would have been able to replicate them or profit from them (Goyal and Welch (2008)). 2
4 Taken together, our findings point to a fundamental difference between apartments, retail and industrial properties, where cap rates do forecast returns, versus office buildings, where they do not. This difference provides us with a unique opportunity to investigate under what circumstances valuation ratios of broadly similar assets commercial real estate properties can or cannot predict returns and the growth in cash payouts. To do so, we formulate an underlying structural model for returns and rent growth whose conditional expectations vary over time. An important feature of the model is that it captures the comovement between the timevarying components of expected returns and expected rent growth ((Menzly, Santos, and Veronesi (2004), Lettau and Van Nieuwerburgh (2008), and Koijen and Van Binsbergen (2009)). Such a comovement is not only supported by our data but, as we demonstrate, also generates systematic patterns in the coefficients of predictive regressions. Relying on an identification scheme which makes use of the estimated predictive regression coefficients as well as other moments of the data, we explicitly relate the predictive regression coefficients to the stochastic properties of returns and rent growth. By doing so, we are able to explain observed differences in the forecasting ability of cap rates across property types in terms of the underlying data generating processes. The ability of the cap rate to forecast returns or rent growth depends primarily on two factors: the comovement between expected returns and expected rent growth, and the extent to which variation in expected rent growth is orthogonal to the timevarying component of expected returns. Interestingly, the comovement factor has a nonmonotonic effect on the predictive regressions slope coefficients. This reflects the fact that a greater comovement reduces both the variability of the cap rate as well as its covariance with future returns. Variation in expected rent growth orthogonal to the timevarying component of expected returns represents noise in the cap rate s ability to forecast returns. If cap rates are driven primarily by this orthogonal component then the cap rate s ability to forecast returns will be reduced while, at the same time, its ability to forecast rent growth will be improved. Because the cap rate is correlated with both expected returns and expected rent growth, this predictor is imperfect as in Pastor and Stambaugh (2009). However, unlike their reducedform setup where expected returns are imperfectly correlated with a predictor, we follow Lettau and Van Nieuwerburgh (2008) and explicitly link the structural parameters of the data generating process to the coefficients of the predictive regression. We find that offices are characterized by the largest comovement between expected returns and expected rent growth and also have a relatively large noise component when compared to the other property types. These two features imply that office cap rates are an imperfect and extremely noisy proxy of future returns. This lack of predictability, however, does not mean that the expected return to offices is not time varying. To the contrary, we document that commercial real estate expected returns and expected rent growth are extremely volatile across all property types. In particular, the variability of realized returns accounted for by the variability of expected 3
5 returns over the 1985 to 2002 sample period range from approximately 16% in the case of industrial properties to almost 30% in the case of retail properties. For rent growth rates over this same sample period, approximately 22% of the variability of realized industrial rent growth rates is explained by the variability of expected industrial rent growth rates, while, at the other extreme, expected office rent growth rates explain almost 43% of the variability of realized office rent growth rates. Our empirical methodology differs in a number of ways from the standard approach of estimating predictive regressions by ordinary least squares (OLS). In particular, we rely on a generalized method of moments (GMM) procedure in which the present value constraint is imposed to jointly estimate the returns and rent growth predictive regressions. This restriction renders the system internally consistent as these regressions are explicitly related by the Campbell and Shiller (1988b) loglinearization. The predictive relations at all horizons are then estimated simultaneously as a system as opposed to horizon by horizon. We also use the entire crosssection of metropolitan areas when estimating the system for each commercial property type. Combining crosssectional and timeseries information improves the efficiency with which the predictive relations will be estimated. Finally, we rely on a doubleresampling procedure to take into account the overlapping and crosssectional nature of our data. The view of commercial real estate that emerges from our analysis is that of an asset class characterized by fluctuations in expected returns not unlike that of common stock. This being the case, a natural question to ask is whether, like common stock, the allocation of commercial real estate within a portfolio can be improved by exploiting the time variation of its expected return. To do so, we use the parametric portfolio approach of Brandt and SantaClara (2006) to investigate the properties of a dynamic portfolio strategy in which funds are allocated between Treasury bills, common stock, and commercial real estate by taking advantage of the information provided by the dividendprice ratio as well as the cap rate. Including the cap rate in addition to the dividend yield has a significant impact on the dynamic asset allocation. In particular, the resultant dynamic portfolio strategy results in an increase of the Sharpe ratio from approximately 0.5 to almost 1.0 in comparison to the corresponding static portfolio position (which ignores predictability) and yields a certainty equivalent return of over 6 percent per year. The plan of this paper is as follows. In Section 2, we present our commercial real estate valuation framework and the corresponding predictive regressions used to investigate the dynamics of commercial real estate returns and rent growth. The timeseries and crosssectional properties of our transactionsbased commercial real estate data are also presented. These properties motivate an underlying structural model of the commercial real estate data generating process. The predictive regression coefficients can then be interpreted in terms of the properties of commercial real estate returns and rent growth implied by the structural model. Section 3 details a twostep estimation procedure which takes advantage of the pooled nature of our data to efficiently estimate predictive 4
6 regressions. The results of estimating insample the predictive regressions and the corresponding structural parameters are then presented. In section 4, we investigate crosssectional differences in our predictive regression results based on population density and land use regulation. We also test the robustness of our results to the inclusion of other crosssectional determinants of commercial real estate returns and rent growth across metropolitan areas. Section 5 investigates the properties of a dynamic portfolio strategy which exploits the predictability of commercial real estate returns as well as the predictability of common stock returns. We offer concluding remarks in Section 6. 2 Commercial Real Estate Returns and Rents 2.1 The Cap Rate Model We denote by P m i,t the price of a commercial property in area i at the end of period t where the superscript m refers to the type of property being considered: apartments, office buildings, industrial, or retail properties. 1 Similarly, H m i,t+1 is the net rent2 of a commercial property of type m in area i from period t to t+1. The gross return from holding a given commercial property from t to t + 1 is defined by: 1 + R m i,t+1 P i,t+1 m + Hm i,t+1 Pi,t m. (1) The definition of the return to commercial real estate is similar to that of common stock. The only difference is that a commercial property pays rental income instead of a dividend. The renttoprice ratio Hi,t m/p i,t m, known as the cap rate in the commercial real estate industry (Geltner and Miller (2000), Brueggeman and Fisher (2008)), corresponds to the dividendprice ratio for stocks. We define the log price, log return, log rent, and log renttoprice ratio as p m i,t log(p m i,t ), ri,t+1 m log(1 + Rm i,t+1 ), hm i,t+1 log(hm i,t+1 ), and capm i,t h m i,t pm i,t, respectively. We follow Campbell and Shiller (1988b) and express ri,t+1 m using a firstorder Taylor approximation as ri,t+1 m κ+ρpm i,t+1 +(1 ρ)hm i,t+1 pm i,t, where κ and ρ are parameters derived from the linearization.3 Solving this relation forward, imposing the transversality condition lim k ρ k p m i,t+k = 0 to avoid the presence of rational bubbles, and taking expectations at time t, we can write the following 1 Hotel properties represent another category of commercial real estate. Unfortunately, we do not have data on hotels and so they are excluded from our subsequent analysis. However, hotels represent less than four percent of the total value of U.S. commercial real estate. See Case (2000). 2 Net rents require the tenant, as opposed to the landlord, to be responsible for operating expenses such as electricity, heat, water, maintenance, and security (see Geltner and Miller (2000)). When there is no possibility of confusion, we will refer to net rents simply as rents. 3 In particular, ρ 1/(1 + exp(h p)) where h p denotes the average log rent  price ratio. Note that for the US commercial real estate market, the average rent  price ratio across property types and metropolitan areas for the sample period is approximately 9% on an annual basis, implying an annualized value for ρ of This is lower than the 0.98 annualized value of ρ for the aggregate stock market during the same period. 5
7 expression for the log cap rate: [ cap m i,t = κ ] [ 1 ρ + E ] t ρ k ri,t+1+k m E t ρ k h m i,t+1+k. (2) k=0 It should be noted that this log linearization is valid only if expected returns and rent growth rates are both stationary. Whether or not this is the case in our commercial real estate data will be investigated later. The preceding expression for the cap rate is best understood as a consistency relation. If a commercial property s cap rate is high, then either the property s expected return is high, or the growth of its rents is expected to be low, or both. This loglinearization framework was proposed by Campbell and Shiller as a generalization of Gordon s (1962) constantgrowth model and explicitly allows both expected returns and dividend growth rates to be timevarying. Like other assets, there are good reasons to believe that expected returns to commercial real estate and rent growth rates are both timevarying. We use expression (2) as the starting point for our analysis of fluctuations in commercial real estate prices. 4 For a particular property type in a specific area, expression (2) states that the cap rate forecasts either expected returns or expected growth in rents, or both. This is usually tested by estimating the following system: k=0 r t+1 = α + β (cap t ) + ε r t+1 (3) h t+1 = µ + λ (cap t ) + ε h t+1 (4) cap t+1 c = φ (cap t c) + ε c t+1. (5) Expressions (3) and (4) are predictive regressions which relate future returns and rent growth, respectively, to today s cap rate while expression (5) describes the dynamics of the cap rate. We collect the residuals of these regressions in the vector ε t+1 = [ε r t+1, εh t+1, εc t+1 ] and denote its variancecovariance matrix by Σ ε. Predictive regressions have been extensively analyzed in the context of the stock market by, among others, Campbell and Shiller (1988b), Fama and French (1988), Cochrane (2008), and Lettau and Van Nieuwerburgh (2008). As emphasized by this literature, absent any further assumptions, the residuals ε t+1 have no clear economic interpretation and are simply forecasting or measurement errors. In the same spirit, expressions (3)(5) are best interpreted as the reduced form of an underlying data generating process that is usually left unspecified. Like much of the predictability literature, we estimate these regressions insample. That is, 4 To the extent that this expression holds for any property type in any particular area, without loss of generality, we will simplify our subsequent notation by simply keeping track of the time subscript. 6
8 our estimates of the parameters of these predictive regressions are based on the entire sample and not just the data available at the time a particular cap rate observation is realized. Therefore, as emphasized by Goyal and Welch (2008), these results be taken as documenting expost variation in conditional means rather than an exante forecasting relation. An important insight of the predictability literature is that the forecasting ability of a slowly moving predictor may be more easily discerned at long horizons as opposed to short horizons. That being the case, we will test whether cap rates forecast future returns and rent growth over a horizon of k > 1 periods: r i,t+1 t+k = α k + β k (cap t ) + ε r t+1 t+k (6) h i,t+1 t+k = µ k + λ k (cap t ) + ε h t+1 t+k (7) where r t+1 t+k k i=0 r t+1+i and h t+1 t+k k i=0 h t+1+i proxy for expected returns and expected rent growth rates, respectively. Under the assumption that the cap rate follows an AR(1) process with autoregressive coefficient φ, as described by expression (5), the shorthorizon and corresponding longhorizon coefficients of the predictive regressions 5 are related by: ( ) 1 φ k β k = β 1 φ and ( ) 1 φ k λ k = λ. (8) 1 φ We will be able to gain further economic insights into the results of these predictive regressions if additional structure is imposed on the dynamics of returns and rent growth rates. To do so requires that we first introduce our commercial real estate data and describe its timeseries and crosssectional properties. 2.2 Commercial Real Estate Data Our commercial real estate data consists of prices, Pi,t m, and cap rates, CAP i,t m, of class A offices, apartments, retail and industrial properties located in fiftythree U.S. metropolitan areas and are provided by Global Real Analytics (GRA). The prices and cap rates for each property type in a particular area are valueweighted averages of corresponding transactions data in a given quarter. 6 Class A buildings are investmentgrade properties that command the highest rents and sales prices in a particular market. 7 The fiftythree sampled areas encompass more than 60% of the U.S. population. A listing of these metropolitan areas is given in Appendix A. The data are available 5 In what follows, the coefficients β and λ always refer to the corresponding oneperiod regression coefficients, while the subscript k applies to longhorizon regression coefficients. 6 GRA will not disclose details surrounding the construction of their data series apart from the fact that all averages for a particular property type are valueweighted and are based on at least twelve transactions within a metropolitan area in a given quarter. Cap rates are calculated based on net rents. 7 Class B buildings, by contrast, are less appealing and are generally deficient in floor plans, condition and facilities. Class C buildings are older buildings that offer basic services and rely on lower rents to attract tenants. 7
9 on a quarterly basis beginning in the second quarter of 1994 (1994:Q2) and ending in the first quarter of 2003 (2003:Q1). Taken together, we have panel data consisting of 1908 observations (36 quarters 53 metropolitan areas). 8 We use the given P m i,t and CAP m i,t to construct quarter t s net rents as Hm i,t = (CAP m i,t P m i,t )/4.9 The gross returns 1+R m i,t in quarter t are then obtained from expression (1) while Hm i,t /Hm i,t 1 gives one plus the growth in rents. For consistency, we work with log cap rates, cap m i,t = ln(cap m i,t ), and log rent growth rates, h m i,t = ln(hm i,t /Hm i,t 1 ). We also rely on log excess returns, rm i,t = ln(1 + R m i,t ) ln(1 + TBL t), where TBL denotes the three month Treasury bill yield. 10 Our returns and rent growth series are based exclusively on transactions data and are available across a crosssection of metropolitan areas. By concentrating only on class A buildings, GRA attempts to hold property quality constant both within a particular metropolitan area as well as across metropolitan areas. 11 While these particular indices are no longer publicly available, they serve as the basis of GRA s recent efforts in conjunction with Standard & Poor s to offer a series of commercial real estate indices for the trading of commercial real estate futures and options on futures on the Chicago Mercantile Exchange. Table 1 presents summary statistics of the key variables in our analysis  excess returns, rent growth rates, and cap rates  during the 1994:Q2 to 2003:Q1 sample period. We report timeseries averages, standard deviations, and serial correlations at both onequarter and oneyear lags. We also report tstatistics testing the null hypotheses of no serial correlation in the excess returns and rent growth series as well as the augmented DickeyFuller (ADF) statistic testing the null hypothesis of a unit root in the cap rate series. In the interest of brevity, we report only the averages of these statistics across the fiftythree sampled metropolitan areas for each of the four commercial property types. From Table 1 we see that the average annualized excess returns of the commercial properties range from 7.3% (offices) to 9.5% (apartments) while the average annualized standard deviations lie between 3.7% (retail) and 6.1% (apartments). By comparison, the corresponding average annualized return of the CRSPZiman REIT valueweighted index is comparable at 8.8% but with a standard deviation of 12.4%. The higher volatility of the REIT index reflects the fact 8 A subset of these data are available for twentyone of the metropolitan areas going back to 1985:Q4 and ending in 2002:Q4 but only at a biannual frequency. 9 We obtain very similar results by modifying the timing convention and relying on the expression Hi,t m = (CAPi,t m Pi,t 1)/4. m 10 We use excess returns throughout the paper, since our main interest is in variation in risk premia. When we use real rather than excess returns, the results are very similar (see also Cochrane (2008)). For the sake of brevity, excess returns will be referred to simply as returns. 11 Commercial real estate turns over far less frequently than residential real estate. This extremely low turnover rate, especially in certain metropolitan areas, makes it difficult to construct a repeatsales index for commercial properties. 8
10 that REITs are leveraged investments that are traded much more frequently than commercial real estate properties. 12 The commercial property excess return series have low serial correlations at a onequarter lag and virtually none at a yearly lag. For each property type, the average serial correlation at a onequarter lag is not statistically significantly different from zero. The number of significant onequarter autocorrelations for any particular property type located in a given metropolitan area (not displayed) is small. Only for offices is the average serial correlation at a onequarter lag relatively high but it remains statistically indistinguishable from zero. At an annual lag, the excess return series are, on average, close to uncorrelated for all property types. Similarly, very few oneyear autocorrelations for a particular property type located in a given metropolitan area are statistically significant (not displayed). While serial correlation tests may have little power, the general message that emerges is that these excess returns do not appear to suffer from the high autocorrelations which plague appraisalbased series. 13 The autocorrelation properties of the rent growth series are similar, exhibiting modest serial correlations at both onequarter and oneyear lags. The lack of persistence in the excess returns and rent growth series can also be seen in the respective values of the tstatistics given in the final column of Table 1 which indicate that we cannot reject the null hypothesis of zero firstorder autocorrelations in either series. Turning our attention to cap rates, the annualized average cap rates in Table 1 range from 8.9% (apartments) to 9.3% (retail) and lie between the estimates of Liu and Mei (1994), who report average cap rates for commercial real estate of approximately 10.4%, and Downing, Stanton, and Wallace (2008) s range of 7.8% to 8.5%. 14 In contrast to the excess return series, however, the cap rate series are extremely persistent. The average firstorder serial correlation at a quarterly lag lies between (industrial) and (offices) and we obtain serial correlation estimates close to unity for commercial properties located in many metropolitan areas (not displayed). The final column of Table 1 reports the average ADF statistic under the null hypothesis of a unit root in the cap rate series. As can be seen, this null hypothesis cannot be rejected for any of the property types, though we also cannot reject localtounity alternatives such as φ = The timeseries properties of the cap rates have important implications for our subsequent 12 During the same sample period, the annualized return of the CRSP valueweighted stock market index had a mean and standard deviation of 8.4% and 19.2%, respectively, while the annualized threemonth Treasury bill rate had a mean and standard deviation of 4.5% and 0.7%, respectively. 13 See Geltner (1991) for a detailed discussion of this issue. 14 The average dividendprice ratio for the CRSPZiman REIT ValueWeighted Index over this sample period is 6.8%. 15 These φ estimates also suffer from a downward bias (Andrews (1993)) which our subsequent estimation procedure must address. 9
11 empirical analysis. In particular, it is well known that persistence in a forecasting variable complicates the estimation of a predictive regression. In addition, any nonzero correlation between shocks to the predictor variable and shocks to the dependent variable induces a bias in the slope estimate of a predictive regression. Several papers including, among others, Stambaugh (1999), Nelson and Kim (1993), Lewellen (2004), Torous, Valkanov, and Yan (2005), and Paye and Timmermann (2006), address these and other issues in the estimation of a predictive regression. This research demonstrates that firstorder asymptotic normality results are not reliable when applied to predictive regressions in small samples. While several improvements in estimating predictive regressions have been suggested, these improvements are difficult to apply in our setting because of the panel nature of our data as well as our relatively short sample period. In addition, we do not have an i.i.d. crosssectional sampling scheme as is usually assumed in panel data studies. For these reasons, our estimation of predictive regressions will rely on a double resampling procedure which takes into account the bias inherent in the predictive regression s slope estimate, the overlapping nature of long horizon regressions, and the crosssectional correlation in cap rates across metropolitan areas. This procedure, which extends Nelson and Kim (1993) s approach to a panel data setting, allows us to address these various estimation issues while directly accounting for our small sample size by relying on a bootstrap methodology. An alternative approach to deal with the persistence of a predictor variable in a predictive regression is to argue that this persistence reflects occasional structural breaks in the series (Paye and Timmermann (2006) and Lettau and Van Nieuwerburgh (2008)). For example, Lettau and Van Nieuwerburgh (2008) identify breaks in the aggregate stock market s dividend yield series and demonstrate that accounting for these breaks has an important effect on the stochastic behavior of the series and, more importantly, on predictability tests. We also test for structural breaks in our cap rate series by property type using Perron s (1989) supf test for breaks with unknown location. We consider both our main 1994:Q2 to 2003:Q1 sample period as well as the extended 1985:Q4 to 2002:Q4 sample period. Only in the case of office properties over the extended sample period do we find evidence of a statistically significant break in cap rates. This break, identified in 1992, corresponds to the well documented collapse in the U.S. office property market in the early 1990s. 16 The top panel of Figure 1 compares cap rates of commercial real estate on a national basis (solid line) with the dividendprice ratio of the stock market (dashed line) over the 1994:Q2 to 2003:Q1 sample period. The national commercial real estate cap series is calculated as the simple average of each of the four property type s national cap rate defined as a populationweighted 16 The difference in average office cap rates before versus after the estimated break is +0.78%. This result is consistent with, for example, the 24% drop in the level of the NCREIF office index between 1991 and No other NCREIF property index experienced a similar drop around this time period. 10
12 average of the corresponding cap rates in the various metropolitan area. 17 The stock market s dividendprice ratio is measured by the dividend price ratio of the CRSP valueweighted index. The average national cap rate is 9.1% while the average dividendprice ratio of the stock market over the same period is 1.7%. The bottom panel shows the same series on a biannual basis for the 1985:Q4 to 2002:Q4 sample period, where the dividendprice ratio series is breakadjusted in 1992 following the approach of Lettau and Van Nieuwerburgh (2008). 18 As can be seen, the stochastic properties of the two series are remarkably similar. In fact, the correlation between the stock market s dividendprice ratio and the national cap rate is for the 1994:Q2 to 2003:Q1 period and during the 1985:Q4 to 2002:Q4 period. This high correlation suggests that, at least at the aggregate level, the stock market and the commercial real estate market are influenced by common factors. To investigate their crosssectional properties, Figure 2 plots the crosssectional distribution of cap rates for each of the four property types. The figure displays mean cap rates as well as their 5 th and 95 th percentiles across the fiftythree metropolitan areas. As can be seen, cap rates exhibit considerable crosssectional variation. For example, the average crosssectional standard deviation in cap rates for offices is 0.58%, which is more than one and a half times the corresponding average timeseries standard deviation of 0.37%. The average difference between the 5 th and 95 th percentiles of these distributions provides another measure of the crosssectional variation in cap rates. In the case of apartments, the average difference between the 5 th and 95 th percentiles is 1.8% which is large when we recall that the average cap rate for apartments across metropolitan areas is 8.9%. This average difference is the largest for offices at 2.1%. Finally, we can also measure the crosssectional dispersion in cap rates by looking at the average R 2 from regressing the individual cap rates on the national average for each corresponding property type. Consistent with the previous findings, the average R 2 is lowest for offices at 0.26 while increasing to 0.36 and 0.46 for industrial and retail properties, respectively. Even in the case of apartments, which display the highest degree of crosssectional dispersion, the average R 2 is only To the extent that this considerable dispersion in cap rates reflects differences in expectations about future returns or rent growth rates across metropolitan areas, it represents valuable crosssectional information which we can exploit to improve the results of our predictability tests. 2.3 Expected Returns and Expected Growth in Rents Guided by these empirical properties, we now impose additional structure on our specification of commercial property returns and rent growth processes. The resultant framework allows us to not 17 Calculating the national cap rate as an average of equally weighted series gives a very similar picture. 18 The national commercial real estate cap series does not exhibit any statistically significant breaks. 11
13 only investigate in more detail the economic properties of our commercial real estate data but also to link the reducedform predictive regressions to an underlying structural model. This approach is used by Lettau and Van Nieuwerburgh (2008) to model aggregate stock market returns. In particular, we assume r t+1 = r + x t + ξt+1 r (9) h t+1 = g + τx t + y t + ξt+1 h (10) where ξt+1 r represents an unexpected shock to commercial real estate returns and ξh t+1 unexpected shock to rent growth with E t (ξt+1 r ) = E t(ξt+1 h ) = 0. Taking expectations, gives is an E t r t+1 E t h t+1 = r + x t = g + τx t + y t where the variables x t and y t capture time variation in expected returns and expected rent growth, respectively. Notice that x t also enters into the equation describing expected rent growth. This will allow us to investigate whether expected returns and expected rent growth are correlated in the commercial real estate market. We model the variations x t and y t as meanzero first order autoregressive processes: x t+1 = φx t + ξ x t+1 (11) y t+1 = φy t + ξ y t+1 (12) where ξt+1 x and ξy t+1 are mean zero innovations in expected returns and expected rent growth, respectively. 19 The system of equations (9)(12) represents the structural model underlying the reducedform predictive regressions. The four structural shocks of the system will be collected in the vector ξ t+1 = [ξ r t+1, ξh t+1, ξx t+1, ξy t+1 ] and the variances of these shocks are denoted by σ2 ξ r, σ2 ξ h, σ 2 ξ x, and σξ 2 y, respectively. The covariance structure of the structural model s shocks must be consistent with the loglinearized cap rate formula given by expression (2). In particular, Campbell s (1991) variance decomposition implies that the structural shocks must satisfy: ξ r t+1 = ρ [ (τ 1)ξ x 1 ρφ t+1 + ξ y ] t+1 + ξ h t+1 (13) 19 For simplicity, we assume that the autoregressive coefficients of the x and y processes are the same and are constant across the different metropolitan areas. While introducing areaspecific φ values is an appealing extension, it would require the estimation of a much larger number of parameters which is not possible given our limited data. The modest crosssectional variation in the cap rate s AR(1) coefficient across areas (not reported) suggests that such heterogeneity is not likely to be a firstorder effect. 12
14 which guarantees identification of the structural model under the assumptions used to derive expression (2). Since expression (13) imposes one restriction among the four structural shocks, we must characterize the covariance structure of three of these shocks. To identify x t+1 and y t+1, we assume that their respective shocks are uncorrelated at all leads and lags, Cov(ξ y t+1, ξx t+j ) = 0, j. In addition, we assume that Cov(ξt+1 h, ξx t+j ) = 0 j, Cov(ξh t+1, ξy t+j ) = 0 j 1, and Cov(ξt+1 h, ξy t+1 ) = ϑ. Imposing these assumptions on the covariance structure of the three unique shocks in ξ t+1 allow us to identify τ as the impact of the expected return component x t+1 on rent growth conditional on y t+1. That is, τ captures any comovement between expected returns and rent growth. For τ = 0, the time variation in expected returns does not influence rent growth, while for τ = 1, they move one for one. From these identifying assumptions, we can see that the variable y t represents fluctuations in expected rent growth that are orthogonal to expected returns. Using expressions (11) and (12), the cap rate can now be written as: cap t = r g 1 ρ ρφ [x t(1 τ) y t ]. (14) The first term in expression (14) reflects the difference between the unconditional expected return and the unconditional rent growth rate. The second term captures the influence of timevarying fluctuations in expected returns and rent growth rates on the cap rate. In particular, large deviations from the unconditional expected return (large x t ) or more persistent deviations (large φ) imply higher cap rates. Also, fluctuations in expected rent growth that are orthogonal to expected returns (y t ) are negatively correlated with cap rates. Finally, the autoregressive structure imposed on expected returns and expected rent growth implies that the cap rate itself follows an AR(1) process with autoregressive coefficient φ (see the proof in Appendix B). We can now explicitly relate the parameters of the reducedform predictive regressions in expressions (3)(4) to the structural parameters of the data generating system, expressions (9) (12). 20 In particular, we can express the oneperiod predictive regression slope coefficients as follows: β = λ = (1 ρφ) (1 τ) + υ 1 1 τ (1 ρφ) [τ(τ 1) + υ] (1 τ) 2 + υ (15) (16) where υ = σ 2 ξ y/σ2 ξ x captures the strength of the orthogonal shocks ξy in expected rent growth relative to the expected return shocks ξ x. 20 All proofs are provided in Appendix B. 13
15 This result makes it clear that it is the combined effect of the structural parameters τ and υ which determines the sign and magnitude of the oneperiod predictive regression slope coefficients. 21 To better see this, the top two panels of Figure 3 plot the predictive coefficients β and λ for values of τ ranging between 1 and 1 given three empirically relevant υ values. The case τ = 0 corresponds to the common assumption made in the asset pricing literature (e.g., Campbell and Shiller (1988a), Cochrane (2008)) that expected returns do not affect cash flow growth rates. In this case, we see from expression (14) that the cap rate will be correlated with expected returns and expected rent growth rates. The oneperiod predictive slope coefficient from the return forecasting regression, expression (15), will be positive for τ = 0 while the corresponding coefficient from the rent growth forecasting equation, expression (16), will be negative. By contrast, for τ = 1, expected rental growth rates move one for one with expected returns and the cap rate in expression (14) will be unable to detect fluctuations in expected returns, β = 0, because the variation in expected returns will be exactly offset by corresponding fluctuations in expected rent growth rates. This can also be seen from expression (15) where β = 0 for τ = 1. In this case, however, λ remains negative because the cap rate is still negatively related to the future growth in rents, expression (14). 22 The link between return predictability and cash flow predictability, discussed recently by, among others, Cochrane (2008) and Lettau and Van Nieuwerburgh (2008), is also evident in the top two panels of Figure 3. For each value of υ, we see that as return predictability increases from τ = 0 through approximately τ = 0.5, the rent growth rate predictability coefficient λ decreases in absolute value. The opposite holds for subsequent τ values. In other words, for given values of the structural parameters, we must either observe return predictability, or rent growth predictability, or both. This result is a restatement of the present value relation (13) which, as pointed out in the context of the aggregate stock market by Lettau and Van Nieuwerburgh (2008), can also be expressed as a restriction between the predictive regression coefficients β and λ: β λ = 1 ρφ. (17) This economic restriction also accounts for the similarity of the plots in the top two panels of Figure 3 as the difference between β and λ must equal a constant for all values of the underlying structural parameters τ and υ. The effects of the structural parameter υ on the reducedform parameters are explored in 21 We do not discuss the roles of the parameters φ and ρ because the former specifies the dynamics of an exogenous variable while the latter is a loglinearization constant which depends on the average cap rate and is seen to display little variation across property types (Table 1). In addition, notice from expressions (15) and (16) that as long as expected returns are stationary ( φ < 1), the quantity (1 ρφ) simply acts as a positive scaling quantity. This implies that φ and ρ do not affect the signs of the slope coefficients. 22 While negative values of τ are theoretically possible and are displayed in Figure 3, we will see that the τ estimates for our commercial real estate data suggest that expected returns and expected rental growth rates are positively correlated. 14
16 the bottom two panels of Figure 3 for three empirically relevant τ values. Since υ is defined as the strength of the orthogonal shocks in expected rent growth relative to expected return shocks, it plays an important role in determining the magnitude of β as well as the magnitude and sign of λ. 23 In the return predictability regression, υ can be interpreted as a noisetosignal ratio as its numerator σ 2 ξ y captures the variation in ξ y orthogonal to expected return fluctuations. As υ increases, the signal from timevarying expected returns is dominated by orthogonal fluctuations in expected rent growth and return predictability becomes difficult to detect. Consequently, β decreases towards zero. By contrast, in the rent growth predictability regression, υ plays exactly the opposite role. It can now be interpreted as a signaltonoise ratio because σξ 2 y captures the signal in the regression predicting rent growth rates. Therefore, as υ increases, predictions in the rent growth regressions become sharper. Explicitly linking the underlying structural parameters to the predictive regression s reducedform coefficients has economic as well as econometric advantages. In particular, the constraint given by expression (17) provides a link between the reducedform estimates and the underlying structural model, thus allowing us to identify the sources of predictability. 24 We can also exploit two important restrictions which follow from this analysis in our empirical work. First, imposing this constraint allows us to jointly estimate the oneperiod predictive regression coefficients β and λ. Second, since the oneperiod predictive regression coefficients β and λ are related to the corresponding longhorizon predictive regression coefficients β k and λ k by expression (8), we will impose these crossequation restrictions at a given horizon as well as across horizons in estimating β and λ. Both of these restrictions will lead to efficiency gains which takes on additional importance given our limited sample period. From the system of expressions (9)(13), we can also derive the proportion of the variance of returns and rent growth due to timevariation in their unobservable expectations. These statistics correspond, respectively, to the R 2 s obtained when regressing realized returns on E t r t+1 (denoted by R 2 Er ), and realized rent growth rates on E t h (denoted by R 2 E h ). Koijen and Van Binsbergen (2009) propose these measures in their investigation of stock market predictability. While the identification and estimation of their underlying structural model differs from ours, using similar R 2 based statistics will allow us to compare the observed time variation in commercial real estate to that of common stock. 23 We restrict our attention to the economically relevant case of υ > 0. In the degenerate case υ = 0, the expected growth in rents is entirely driven by shocks to expected returns when there are no orthogonal shocks to expected rent growth. 24 It should be noted that the identification of the structural parameters relies on the assumption that agents are forming their expectations rationally. If this were not the case, the Campbell and Shiller (1988b) decomposition ceases to be a valid description of the underlying data generating process as it would suffer from an omitted variable bias. This, in turn, would bias the interpretation of the structural parameters, but not the results from estimating the predictive VAR, equations (35). 15
17 It is important to realize that the statistics R 2 Er and R2 E h are based on the structural relations posited to prevail in the commercial real estate market. Therefore, they may differ substantially from those calculated in simple predictive regressions, such as expressions (3) and (4). To see the difference, consider the extreme case where expected returns and expected rent growth rates are timevarying and highly correlated so that τ = 1. Under this assumption, the cap rate will be unable to forecast future returns despite the fact that expected returns are timevarying and the R 2 of the predictive regression (3) will be zero. However, R 2 Er will be nonzero in this case and will be able to properly measure the magnitude of timevariation in expected returns. 3 Empirical Results 3.1 Estimation Method We use a Generalized Method of Moments (GMM) procedure to estimate the longhorizon predictive regressions, expressions (6) and (7), by imposing both the present value restriction, expression (17), as well as the restriction between shorthorizon and longhorizon coefficients given in expression (8). We estimate these regressions insample at forecast horizons of k =1, 4, 8 and 12 quarters and the moments we use are the standard OLS orthogonality conditions. Taken together, we have a total of eight equations (four horizons for each of the two regressions) and two unknowns (β and λ). We rely on the pooled sample of fiftythree metropolitan areas over the 1994:Q2 to 2003:Q1 sample period for each of the four commercial property types. It is important to emphasize that our pooled regressions differ from the timeseries regressions used in the stock return predictability literature. Given the limited time period spanned by our data, this pooled approach has a number of advantages. Because we are primarily interested in longhorizon relations but, unfortunately, do not have a sufficiently long time series, the only statistically reliable means of exploring these relations is to rely on pooled data. Also, as previously demonstrated, there is considerable heterogeneity in returns, rent growth rates, and cap rates across metropolitan areas at any particular point in time. Therefore, tests based on the pooled regressions are likely to have higher power than tests based on timeseries regressions in which the predictive variable has only a modest variance (Torous and Valkanov (2001)). Before presenting our results, we address a number of statistical issues concerning our pooled predictive regression framework. First, the overlap in longhorizon returns and rent growth rates must be explicitly taken into account. In our case, this overlap is particularly large relative to the sample size. In addition to inducing serial correlation in the residuals, this overlap induces persistence in the regressors and, as a result, alters their stochastic properties. While this problem 16
18 has been investigated in the context of timeseries regressions, it is also likely to affect the smallsample properties of the estimators in our pooled regressions. Second, the predictors themselves are crosssectionally correlated. By way of example, the median crosssectional correlation of apartment cap rates in our sample is and is as high as (between Washington, DC and Philadelphia). Because we effectively have fewer than fiftythree independent cap rate observations at any particular point in time, a failure to account for this crosssectional dependence will lead to inflated tstatistics. Finally, the cap rates are themselves persistent and their innovations are correlated with the return innovations. Under these circumstances, it is well known that, at least in smallsamples, least squares estimators of a slope coefficient will be biased in timeseries predictive regressions (Stambaugh (1999)). In pooled predictive regressions, the slope estimates will also exhibit this bias because they are effectively weighted averages of the biased slope estimates of the timeseries predictive regressions for each metropolitan area. As a result of these statistical issues, traditional asymptotic methods are unlikely to provide reliable inference in our pooled predictive regression framework. As an alternative, we rely on a twostep resampling approach. In the first step, as is customary when estimating any predictive regression, we run timeseries regressions for each of the fiftythree metropolitan areas in which oneperiod returns and rent growth rates are individually regressed on lagged cap rates while the cap rates themselves are regressed on lagged cap rates. The coefficients and residuals from these regressions are subsequently stored. For each area we then resample the return residuals, rent growth residuals and cap rate residuals jointly across time (without replacement, as in Nelson and Kim (1993)). The randomized return and rent growth residuals are used to create oneperiod returns and rent growth rates, respectively, under the null of no predictability. To generate cap rates, we use the corresponding coefficient estimates together with the resampled residuals from the cap rate autoregression. For each resampling i, we then form overlapping multiperiod returns and rent growth rates from the resampled singleperiod series and obtain GMM estimates (ˆβ i, ˆλ i ). This first step is used to obtain estimates of the small sample bias of the slope coefficients as the contemporaneous correlations between the return or rent growth residuals and cap rate residuals in a given metropolitan area as well as across areas are preserved. Because these data are generated under the null, the average ˆβ across resamplings, denoted by β = I 1 I ˆβ i=1 i, estimates the bias in the pooled predictive regression. The biasadjusted estimate of β is obtained as ˆβ adj = ˆβ β, where ˆβ is the biased estimate of β obtained from the pooled GMM estimation. The biasadjusted estimate for the rent growth predictive regression, ˆλ adj, is similarly constructed. This procedure is in essence that suggested by Nelson and Kim (1993) but applied to a pooled regression. However, while this procedure captures the overlap in the multiperiod returns, it does not address the crosssectional dependence in cap rates. This then necessitates our second step. To account for the possibility that our predictability 17
19 results are driven by crosssectional correlation in cap rates, we resample the cap rates across metropolitan areas at each point in time for each forecast horizon. 25 Then, for a given crosssection, we estimate the predictive regression using the twostage GMM procedure thus obtaining T estimates ( β s, λ s ), where T is the sample size for which we can construct GMM estimates using all horizons and the superscript s denotes crosssectional estimates from the resampled data. We repeat the entire resampling procedure 1,000 times which gives 1,000 T estimates ( β s, λ s ). We use these 1,000 T estimates to compute standard errors, denoted by se(β) and se(λ), respectively. This second step is very similar to a standard Fama and MacBeth (1973) regression with the exception that we are running the regressions with 1,000 replications of bootstrapped data rather than the original data. The standard errors from the double resampling procedure account for both timeseries and crosssectional dependence in the data. In the first resampling step, the overlapping nature of the regressors is explicitly taken into account, while in the subsequent resampling step, at each point in time the cap rates are drawn from their empirical distribution. The biasadjusted double resampling t statistic, denoted by t DR, is computed as t DR = ˆβ adj /se(β) = (ˆβ β)/se(β), and analogously for λ. The 95 th and 99 th percentiles of the bootstrapped distributions of the t DR statistic are used to assess the statistical significance in our empirical analyses. For the sake of clarity, we report levels of significance next to the estimates (5% and 1%) rather than smallsample critical values because the latter are a function of the overlap as well as the crosssectional cap rate correlations of a particular property type Predictive Regression Results adj adj Table 2 presents the biasadjusted GMM estimates, ˆβ k and ˆλ k, as well as their corresponding t DR statistics for each of the four property types based on the 1994:Q2 to 2003:Q1 sample period. The slope coefficients at the k = 1 quarter horizon and their t DR statistics are obtained directly from the GMM procedure. The longhorizon coefficients for k 4 quarters are then calculated using expression (8) where the required φ value is estimated by substituting the GMM estimates in the present value constraint expression (17). For these longhorizon slope coefficient estimates, the 25 The bootstrap is carried out with replacement. We also attempted resampling without replacement and obtained very similar results. 26 A few additional points are worth mentioning about the our resampling procedure. First, the second bootstrap is necessary in order to take into account the crosssectional correlation in cap rates. Without it, the standard errors would not be corrected for the crosssectional dependence in cap rates. We verified that if we use only the Nelson and Kim (1993) randomization, we obtain t statistics very similar to the Newey and West (1987) results. Second, it is interesting to note that the pooled regression does not produce unbiased estimates. The reason is that given the crosssectional correlation in cap rates and the fact that cap rate fluctuations and return shocks are correlated, the pooled regression effectively yields a weighted average of the biased estimates that would have been obtained in time series regressions for each metropolitan area. Third, the biasadjusted GMM estimates will take into account the fact that the bias tends to be larger at longer horizons, where the sample size is smaller and the overlap is larger. 18
20 t DR statistics are then calculated using the delta method. Statistical significance at the 5% and 1% levels are denoted by superscripts a and b, respectively. For comparison with previous results, we also provide the R 2 statistics for OLS regressions of future returns on log cap rates (R 2 r) and future rent growth on log cap rates (R 2 h ), estimated separately. For all property types, we see that at the short horizon of k = 1 quarter, cap rates are positively correlated with future returns. Retail properties have the largest biasadjusted slope coefficient, ˆβadj = 0.111, and office properties have the smallest, ˆβadj = For all property types except offices, the corresponding biascorrected slope coefficients are statistically significant. Regardless of the property type, however, cap rates explain very little of return variability at the k = 1 quarter horizon as evidenced by the low R 2 r statistics reflecting the large variability in quarterly commercial property returns. ˆβ adj k As the return horizon lengthens, k 4 quarters, the biascorrected slope coefficients increase in magnitude and provide reliable evidence of return predictability in the case of apartments, industrial and retail properties. The predictive regressions also explain an increasingly larger proportion of the variability of these property returns at longer horizons. In the case of retail properties, the biascorrected slope estimate increases to ˆβ adj = at k = 12 quarters where the predictive regression can explain approximately 27% of the variability in returns. The explanatory power of the predictive regressions are somewhat smaller for apartments and industrial properties, explaining 15% of industrial property returns and 17% of apartment returns at the k = 12 quarter horizon. In contrast to the other property types, there does not appear to be reliable evidence of return predictability at any horizon for offices. The biascorrected slope estimates ˆβ adj k for offices are much smaller in magnitude and are never statistically significant. For example, at k = 12 quarters, the slope coefficient is ˆβ adj = 0.247, which is approximately half of the slope coefficient for apartments (0.468) and approximately onequarter of that for retail properties (0.966). The corresponding R 2 r statistics are also small for offices across all horizons, achieving a maximum of only 3.9% at a horizon of k = 8 quarters. Turning our attention to the rent growth results presented in Table 2, it can immediately be seen that there is no reliable evidence that cap rates can forecast the future growth in rents of apartments, industrial and retail properties. Across all horizons, the biascorrected slope coefficients ˆλ adj are not significantly different from zero and the corresponding R 2 h statistics are small, between 0% and 3.1 %. By contrast, in the case of offices, the biascorrected slope coefficients are negative and statistically significant. For example, the slope coefficient is ˆλ adj = with t DR = at a horizon of k = 4 quarters, increasing to ˆλ adj = with t DR = at a horizon of k = 12 quarters. However, the explanatory power of these regressions is small, the R 2 h statistics 19
The CrossSectional Dispersion of Commercial Real Estate Returns and Rent Growth: Time Variation and Economic Fluctuations
The CrossSectional Dispersion of Commercial Real Estate Returns and Rent Growth: Time Variation and Economic Fluctuations Alberto Plazzi Anderson School UCLA and University of Verona Walter Torous Anderson
More informationThe CrossSectional Dispersion of Commercial Real Estate Returns and Rent Growth: Time Variation and Economic Fluctuations
The CrossSectional Dispersion of Commercial Real Estate Returns and Rent Growth: Time Variation and Economic Fluctuations Alberto Plazzi The Anderson School UCLA and University of Verona Walter Torous
More informationDynamics of Commercial Real Estate Asset Markets, Return Volatility, and the Investment Horizon. Christian Rehring* Steffen Sebastian**
Dynamics of Commercial Real Estate Asset Markets, Return Volatility, and the Investment Horizon Christian Rehring* Steffen Sebastian** This version: May 6 200 Abstract The term structure of return volatility
More informationDiscussion of Momentum and Autocorrelation in Stock Returns
Discussion of Momentum and Autocorrelation in Stock Returns Joseph Chen University of Southern California Harrison Hong Stanford University Jegadeesh and Titman (1993) document individual stock momentum:
More informationDividend yields, dividend growth, and return predictability. in the crosssection of stocks
Dividend yields, dividend growth, and return predictability in the crosssection of stocks Paulo Maio 1 Pedro SantaClara 2 First version: June 2012 This version: November 2012 3 1 Hanken School of Economics.
More informationThe VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series.
Cointegration The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series. Economic theory, however, often implies equilibrium
More informationPriceEarnings Ratios: Growth and Discount Rates
PriceEarnings Ratios: Growth and Discount Rates Andrew Ang Columbia University and NBER Xiaoyan Zhang Purdue University This Version: 20 May 2011 We thank Geert Bekaert, Sigbjørn Berg, and Tørres Trovik
More informationSYSTEMS OF REGRESSION EQUATIONS
SYSTEMS OF REGRESSION EQUATIONS 1. MULTIPLE EQUATIONS y nt = x nt n + u nt, n = 1,...,N, t = 1,...,T, x nt is 1 k, and n is k 1. This is a version of the standard regression model where the observations
More informationPriceEarnings Ratios, Dividend Yields and Real Estate Stock Prices
PriceEarnings Ratios, Dividend Yields and Real Estate Stock Prices Executive Summary. Both dividend yields and past returns have predictive power for P/E ratios; hence they can be used as tools in forming
More informationWhat Drives REIT Prices? The TimeVarying Informational Content of Dividend Yields
What Drives REIT Prices? The TimeVarying Informational Content of Dividend Yields Kevin C.H. Chiang* This draft: January 31, 2014 * Correspondence: Kevin C.H. Chiang, 315 Kalkin Hall, School of Business
More informationStock market booms and real economic activity: Is this time different?
International Review of Economics and Finance 9 (2000) 387 415 Stock market booms and real economic activity: Is this time different? Mathias Binswanger* Institute for Economics and the Environment, University
More informationDividend Yields, Dividend Growth, and Return Predictability in the Cross Section of Stocks
JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS Vol. 50, Nos. 1/2, Feb./Apr. 2015, pp. 33 60 COPYRIGHT 2015, MICHAEL G. FOSTER SCHOOL OF BUSINESS, UNIVERSITY OF WASHINGTON, SEATTLE, WA 98195 doi:10.1017/s0022109015000058
More informationDividendPrice Ratios and Stock Returns: Another Look at the History
First draft: January 2012 Current version: March 2012 DividendPrice Ratios and Stock Returns: Another Look at the History BRADFORD CORNELL CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA, CA 91125 626 5642001
More informationPredictable Dividends and Returns
Predictable Dividends and Returns Job Market Paper Ruy Ribeiro 1 Graduate School of Business University of Chicago November, 2002 1 Ph.D. Candidate in Finance. Email: ruy.ribeiro@gsb.uchicago.edu. I am
More informationFinancial Assets Behaving Badly The Case of High Yield Bonds. Chris Kantos Newport Seminar June 2013
Financial Assets Behaving Badly The Case of High Yield Bonds Chris Kantos Newport Seminar June 2013 Main Concepts for Today The most common metric of financial asset risk is the volatility or standard
More informationIs the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate?
Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate? Emily Polito, Trinity College In the past two decades, there have been many empirical studies both in support of and opposing
More informationPITFALLS IN TIME SERIES ANALYSIS. Cliff Hurvich Stern School, NYU
PITFALLS IN TIME SERIES ANALYSIS Cliff Hurvich Stern School, NYU The t Test If x 1,..., x n are independent and identically distributed with mean 0, and n is not too small, then t = x 0 s n has a standard
More informationSTOCK MARKET VOLATILITY AND REGIME SHIFTS IN RETURNS
STOCK MARKET VOLATILITY AND REGIME SHIFTS IN RETURNS ChiaShang James Chu Department of Economics, MC 0253 University of Southern California Los Angles, CA 90089 Gary J. Santoni and Tung Liu Department
More informationStock Returns and Equity Premium Evidence Using Dividend Price Ratios and Dividend Yields in Malaysia
Stock Returns and Equity Premium Evidence Using Dividend Price Ratios and Dividend Yields in Malaysia By David E. Allen 1 and Imbarine Bujang 1 1 School of Accounting, Finance and Economics, Edith Cowan
More informationC(t) (1 + y) 4. t=1. For the 4 year bond considered above, assume that the price today is 900$. The yield to maturity will then be the y that solves
Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of longterm fixed income securities are federal government bonds, corporate
More informationYao Zheng University of New Orleans. Eric Osmer University of New Orleans
ABSTRACT The pricing of China Region ETFs  an empirical analysis Yao Zheng University of New Orleans Eric Osmer University of New Orleans Using a sample of exchangetraded funds (ETFs) that focus on investing
More informationWorking Paper No. 520 A forecast evaluation of expected equity return measures Michael Chin and Christopher Polk
Working Paper No. 520 A forecast evaluation of expected equity return measures Michael Chin and Christopher Polk January 2015 Working papers describe research in progress by the author(s) and are published
More informationMODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS
MODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS EIGHTH EDITION INTERNATIONAL STUDENT VERSION EDWIN J. ELTON Leonard N. Stern School of Business New York University MARTIN J. GRUBER Leonard N. Stern School
More informationTime Series Analysis
Time Series Analysis Identifying possible ARIMA models Andrés M. Alonso Carolina GarcíaMartos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 2012 Alonso and GarcíaMartos
More informationIntegrated Resource Plan
Integrated Resource Plan March 19, 2004 PREPARED FOR KAUA I ISLAND UTILITY COOPERATIVE LCG Consulting 4962 El Camino Real, Suite 112 Los Altos, CA 94022 6509629670 1 IRP 1 ELECTRIC LOAD FORECASTING 1.1
More informationInvesting for the Long Run when Returns Are Predictable
THE JOURNAL OF FINANCE VOL. LV, NO. 1 FEBRUARY 2000 Investing for the Long Run when Returns Are Predictable NICHOLAS BARBERIS* ABSTRACT We examine how the evidence of predictability in asset returns affects
More informationFORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits
Technical Paper Series Congressional Budget Office Washington, DC FORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits Albert D. Metz Microeconomic and Financial Studies
More informationTesting for Granger causality between stock prices and economic growth
MPRA Munich Personal RePEc Archive Testing for Granger causality between stock prices and economic growth Pasquale Foresti 2006 Online at http://mpra.ub.unimuenchen.de/2962/ MPRA Paper No. 2962, posted
More informationChapter 6. Econometrics. 6.1 Introduction. 6.2 Univariate techniques Transforming data
Chapter 6 Econometrics 6.1 Introduction We re going to use a few tools to characterize the time series properties of macro variables. Today, we will take a relatively atheoretical approach to this task,
More informationA MeanVariance Framework for Tests of Asset Pricing Models
A MeanVariance Framework for Tests of Asset Pricing Models Shmuel Kandel University of Chicago TelAviv, University Robert F. Stambaugh University of Pennsylvania This article presents a meanvariance
More informationChap 3 CAPM, Arbitrage, and Linear Factor Models
Chap 3 CAPM, Arbitrage, and Linear Factor Models 1 Asset Pricing Model a logical extension of portfolio selection theory is to consider the equilibrium asset pricing consequences of investors individually
More informationTrading Probability and Turnover as measures of Liquidity Risk: Evidence from the U.K. Stock Market. Ian McManus. Peter Smith.
Trading Probability and Turnover as measures of Liquidity Risk: Evidence from the U.K. Stock Market. Ian McManus (Corresponding author). School of Management, University of Southampton, Highfield, Southampton,
More information8.1 Summary and conclusions 8.2 Implications
Conclusion and Implication V{tÑàxÜ CONCLUSION AND IMPLICATION 8 Contents 8.1 Summary and conclusions 8.2 Implications Having done the selection of macroeconomic variables, forecasting the series and construction
More informationChapter 1. Vector autoregressions. 1.1 VARs and the identi cation problem
Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have become
More informationThe equity share in new issues and aggregate stock returns
The equity share in new issues and aggregate stock returns Malcolm Baker Jeffrey Wurgler * October 1, 1999 ABSTRACT The share of equity issues in total new equity and debt issues is a strong predictor
More informationNonlinear Mean Reversion in Stock Prices
Nonlinear Mean Reversion in Stock Prices Sebastiano Manzan CeNDEF, Department of Quantitative Economics, University of Amsterdam Roetersstraat 11, 1018 WB Amsterdam, the Netherlands email: s.manzan@uva.nl,
More informationChapter 4: Vector Autoregressive Models
Chapter 4: Vector Autoregressive Models 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie IV.1 Vector Autoregressive Models (VAR)...
More informationFinancial Time Series Analysis (FTSA) Lecture 1: Introduction
Financial Time Series Analysis (FTSA) Lecture 1: Introduction Brief History of Time Series Analysis Statistical analysis of time series data (Yule, 1927) v/s forecasting (even longer). Forecasting is often
More informationCFA Examination PORTFOLIO MANAGEMENT Page 1 of 6
PORTFOLIO MANAGEMENT A. INTRODUCTION RETURN AS A RANDOM VARIABLE E(R) = the return around which the probability distribution is centered: the expected value or mean of the probability distribution of possible
More informationDiscussion of Which Approach to Accounting for Employee Stock Options Best Reflects Market Pricing?
Discussion of Which Approach to Accounting for Employee Stock Options Best Reflects Market Pricing? David Aboody daboody@anderson.ucla.edu UCLA Anderson School of Management, 110 Westwood Plaza, Los Angeles,
More informationAnalysis of Financial Time Series with EViews
Analysis of Financial Time Series with EViews Enrico Foscolo Contents 1 Asset Returns 2 1.1 Empirical Properties of Returns................. 2 2 Heteroskedasticity and Autocorrelation 4 2.1 Testing for
More informationInternet Appendix to Stock Market Liquidity and the Business Cycle
Internet Appendix to Stock Market Liquidity and the Business Cycle Randi Næs, Johannes A. Skjeltorp and Bernt Arne Ødegaard This Internet appendix contains additional material to the paper Stock Market
More informationDynamic Asset Allocation in Chinese Stock Market
Dynamic Asset Allocation in Chinese Stock Market Jian Chen Fuwei Jiang Jun Tu Current version: January 2014 Fujian Key Laboratory of Statistical Sciences & Department of Finance, School of Economics, Xiamen
More informationThe Term Structure of the RiskReturn Tradeoff
The Term Structure of the RiskReturn Tradeoff John Y. Campbell and Luis M. Viceira 1 Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest
More informationMarketing Mix Modelling and Big Data P. M Cain
1) Introduction Marketing Mix Modelling and Big Data P. M Cain Big data is generally defined in terms of the volume and variety of structured and unstructured information. Whereas structured data is stored
More informationA Trading Strategy Based on the LeadLag Relationship of Spot and Futures Prices of the S&P 500
A Trading Strategy Based on the LeadLag Relationship of Spot and Futures Prices of the S&P 500 FE8827 Quantitative Trading Strategies 2010/11 MiniTerm 5 Nanyang Technological University Submitted By:
More informationAsset Pricing Implications of Firms Financing Constraints.
Asset Pricing Implications of Firms Financing Constraints. Joao F. Gomes, Amir Yaron, and Lu Zhang October 2003 Abstract We use a productionbased asset pricing model to investigate whether financial market
More informationDo Implied Volatilities Predict Stock Returns?
Do Implied Volatilities Predict Stock Returns? Manuel Ammann, Michael Verhofen and Stephan Süss University of St. Gallen Abstract Using a complete sample of US equity options, we find a positive, highly
More informationB.3. Robustness: alternative betas estimation
Appendix B. Additional empirical results and robustness tests This Appendix contains additional empirical results and robustness tests. B.1. Sharpe ratios of betasorted portfolios Fig. B1 plots the Sharpe
More informationStock Return Predictability: Is it There?
Stock Return Predictability: Is it There? Andrew Ang Columbia University and NBER Geert Bekaert Columbia University and NBER This Version: 24 February 2006 We thank Xiaoyan Zhang for help with data. We
More informationMarket Efficiency and Stock Market Predictability
Mphil Subject 301 Market Efficiency and Stock Market Predictability M. Hashem Pesaran March 2003 1 1 Stock Return Regressions R t+1 r t = a+b 1 x 1t +b 2 x 2t +...+b k x kt +ε t+1, (1) R t+1 is the oneperiod
More informationThe LifeCycle Motive and Money Demand: Further Evidence. Abstract
The LifeCycle Motive and Money Demand: Further Evidence Jan Tin Commerce Department Abstract This study takes a closer look at the relationship between money demand and the lifecycle motive using panel
More informationA Simple Model of Price Dispersion *
Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price Dispersion
More informationDoes the Early Exercise Premium Contain Information about Future Underlying Returns?
Does the Early Exercise Premium Contain Information about Future Underlying Returns? Rossen Valkanov The Rady School UCSD Pradeep Yadav Price College of Business University of Oklahoma Yuzhao Zhang The
More informationFinancial TIme Series Analysis: Part II
Department of Mathematics and Statistics, University of Vaasa, Finland January 29 February 13, 2015 Feb 14, 2015 1 Univariate linear stochastic models: further topics Unobserved component model Signal
More informationVOLATILITY FORECASTING FOR MUTUAL FUND PORTFOLIOS. Samuel Kyle Jones 1 Stephen F. Austin State University, USA Email: sjones@sfasu.
VOLATILITY FORECASTING FOR MUTUAL FUND PORTFOLIOS 1 Stephen F. Austin State University, USA Email: sjones@sfasu.edu ABSTRACT The return volatility of portfolios of mutual funds having similar investment
More informationInterpreting Market Responses to Economic Data
Interpreting Market Responses to Economic Data Patrick D Arcy and Emily Poole* This article discusses how bond, equity and foreign exchange markets have responded to the surprise component of Australian
More informationOnline Appendices to the Corporate Propensity to Save
Online Appendices to the Corporate Propensity to Save Appendix A: Monte Carlo Experiments In order to allay skepticism of empirical results that have been produced by unusual estimators on fairly small
More informationHow to assess the risk of a large portfolio? How to estimate a large covariance matrix?
Chapter 3 Sparse Portfolio Allocation This chapter touches some practical aspects of portfolio allocation and risk assessment from a large pool of financial assets (e.g. stocks) How to assess the risk
More informationInternet Appendix to Picking Winners? Investment Consultants Recommendations of Fund Managers
Internet Appendix to Picking Winners? Investment Consultants Recommendations of Fund Managers TIM JENKINSON, HOWARD JONES, and JOSE VICENTE MARTINEZ * This Internet Appendix includes the following additional
More informationHow Much Equity Does the Government Hold?
How Much Equity Does the Government Hold? Alan J. Auerbach University of California, Berkeley and NBER January 2004 This paper was presented at the 2004 Meetings of the American Economic Association. I
More information4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4
4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Nonlinear functional forms Regression
More informationOptimal Consumption with Stochastic Income: Deviations from Certainty Equivalence
Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence Zeldes, QJE 1989 Background (Not in Paper) Income Uncertainty dates back to even earlier years, with the seminal work of
More informationGRADO EN ECONOMÍA. Is the Forward Rate a True Unbiased Predictor of the Future Spot Exchange Rate?
FACULTAD DE CIENCIAS ECONÓMICAS Y EMPRESARIALES GRADO EN ECONOMÍA Is the Forward Rate a True Unbiased Predictor of the Future Spot Exchange Rate? Autor: Elena Renedo Sánchez Tutor: Juan Ángel Jiménez Martín
More informationReal Estate Returns in Public and Private Markets
Real Estate Returns in Public and Private Markets The NCREIF Property Index understates the return volatility of commercial properties. JOSEPH GYOURKO PRIOR TO THE 1990S, commercial real estate was undoubtedly
More informationIntegrating Financial Statement Modeling and Sales Forecasting
Integrating Financial Statement Modeling and Sales Forecasting John T. Cuddington, Colorado School of Mines Irina Khindanova, University of Denver ABSTRACT This paper shows how to integrate financial statement
More informationAsymmetry and the Cost of Capital
Asymmetry and the Cost of Capital Javier García Sánchez, IAE Business School Lorenzo Preve, IAE Business School Virginia Sarria Allende, IAE Business School Abstract The expected cost of capital is a crucial
More informationMeasuring and Modeling Variation in the RiskReturn Tradeoff
Measuring and Modeling Variation in the RiskReturn Tradeoff Martin Lettau New York University, CEPR, NBER Sydney C. Ludvigson New York University and NBER Preliminary Comments Welcome First draft: July
More informationK. V. Kovalevskii ANALYSIS AND COMPARISON OF THE SKILLS OF TWO MUTUAL FUND MANAGERS
K. V. Kovalevskii Graduate Student Durham University Business School ANALYSIS AND COMPARISON OF THE SKILLS OF TWO MUTUAL FUND MANAGERS Abstract. The purpose of this paper is to analyze and compare the
More informationEarnings Announcement and Abnormal Return of S&P 500 Companies. Luke Qiu Washington University in St. Louis Economics Department Honors Thesis
Earnings Announcement and Abnormal Return of S&P 500 Companies Luke Qiu Washington University in St. Louis Economics Department Honors Thesis March 18, 2014 Abstract In this paper, I investigate the extent
More informationThe average hotel manager recognizes the criticality of forecasting. However, most
Introduction The average hotel manager recognizes the criticality of forecasting. However, most managers are either frustrated by complex models researchers constructed or appalled by the amount of time
More informationON THE RISK ADJUSTED DISCOUNT RATE FOR DETERMINING LIFE OFFICE APPRAISAL VALUES BY M. SHERRIS B.A., M.B.A., F.I.A., F.I.A.A. 1.
ON THE RISK ADJUSTED DISCOUNT RATE FOR DETERMINING LIFE OFFICE APPRAISAL VALUES BY M. SHERRIS B.A., M.B.A., F.I.A., F.I.A.A. 1. INTRODUCTION 1.1 A number of papers have been written in recent years that
More informationA Review of Cross Sectional Regression for Financial Data You should already know this material from previous study
A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study But I will offer a review, with a focus on issues which arise in finance 1 TYPES OF FINANCIAL
More informationThe comovement of US and German bond markets
The comovement of US and German bond markets Tom Engsted and Carsten Tanggaard The Aarhus School of Business, Fuglesangs alle 4, DK8210 Aarhus V. Emails: tom@asb.dk (Engsted); cat@asb.dk (Tanggaard).
More informationA Primer on Forecasting Business Performance
A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.
More informationThe Loss in Efficiency from Using Grouped Data to Estimate Coefficients of Group Level Variables. Kathleen M. Lang* Boston College.
The Loss in Efficiency from Using Grouped Data to Estimate Coefficients of Group Level Variables Kathleen M. Lang* Boston College and Peter Gottschalk Boston College Abstract We derive the efficiency loss
More informationDOES IT PAY TO HAVE FAT TAILS? EXAMINING KURTOSIS AND THE CROSSSECTION OF STOCK RETURNS
DOES IT PAY TO HAVE FAT TAILS? EXAMINING KURTOSIS AND THE CROSSSECTION OF STOCK RETURNS By Benjamin M. Blau 1, Abdullah Masud 2, and Ryan J. Whitby 3 Abstract: Xiong and Idzorek (2011) show that extremely
More informationEstimation and Inference in Cointegration Models Economics 582
Estimation and Inference in Cointegration Models Economics 582 Eric Zivot May 17, 2012 Tests for Cointegration Let the ( 1) vector Y be (1). Recall, Y is cointegrated with 0 cointegrating vectors if there
More informationIntroduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
More informationA Transactions Data Analysis of Nonsynchronous Trading
A Transactions Data Analysis of Nonsynchronous Trading Gregory B. Kadlec Douglas M. Patterson Virginia Polytechnic Institute Weekly returns of stock portfolios exhibit substantial autocorrelation. Analytical
More informationThe cross section of expected stock returns
The cross section of expected stock returns Jonathan Lewellen Dartmouth College and NBER This version: August 2014 Forthcoming in Critical Finance Review Tel: 6036468650; email: jon.lewellen@dartmouth.edu.
More informationExcess Volatility and ClosedEnd Fund Discounts
Excess Volatility and ClosedEnd Fund Discounts Michael Bleaney School of Economics University of Nottingham Nottingham NG7 RD, U.K. Tel. (+44) 115 951 5464 Fax (+44) 115 951 4159 email: michael.bleaney@nottingham.ac.uk
More informationThe term structure of equity option implied volatility
The term structure of equity option implied volatility Christopher S. Jones Tong Wang Marshall School of Business Marshall School of Business University of Southern California University of Southern California
More informationEconometric Analysis of Cross Section and Panel Data Second Edition. Jeffrey M. Wooldridge. The MIT Press Cambridge, Massachusetts London, England
Econometric Analysis of Cross Section and Panel Data Second Edition Jeffrey M. Wooldridge The MIT Press Cambridge, Massachusetts London, England Preface Acknowledgments xxi xxix I INTRODUCTION AND BACKGROUND
More informationExamining the Relationship between ETFS and Their Underlying Assets in Indian Capital Market
2012 2nd International Conference on Computer and Software Modeling (ICCSM 2012) IPCSIT vol. 54 (2012) (2012) IACSIT Press, Singapore DOI: 10.7763/IPCSIT.2012.V54.20 Examining the Relationship between
More informationVI. Real Business Cycles Models
VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized
More informationFirm Fundamentals and Variance Risk Premiums
Firm Fundamentals and Variance Risk Premiums Matthew R. Lyle and James P. Naughton August 2015 Abstract We develop and empirically test an accountingbased model that ties two firm characteristics, booktomarket
More informationDoes Mutual Fund Performance Vary over the Business Cycle?
Does Mutual Fund Performance Vary over the Business Cycle? Anthony W. Lynch New York University and NBER Jessica A. Wachter University of Pennsylvania and NBER First Version: 15 November 2002 Current Version:
More informationRedefining Private Equity Real Estate Risk
Redefining Private Equity Real Estate Risk Richard Gold & Emilian Belev December 7, 2010 Northfield Information Services, Inc. 77 North Washington Street 9 th Floor Boston, MA 02114 USA Tel: 617.451.2222
More informationDoes Mutual Fund Performance Vary over the Business Cycle?
Does Mutual Fund Performance Vary over the Business Cycle? Anthony W. Lynch New York University and NBER Jessica Wachter New York University and NBER Walter Boudry New York University First Version: 15
More informationC: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)}
C: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)} 1. EES 800: Econometrics I Simple linear regression and correlation analysis. Specification and estimation of a regression model. Interpretation of regression
More informationSTATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 SigmaRestricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary
More informationDo Industries Lead the Stock Market? Gradual Diffusion of Information and CrossAsset Return Predictability
Do Industries Lead the Stock Market? Gradual Diffusion of Information and CrossAsset Return Predictability Harrison Hong Stanford University Walter Torous UCLA Rossen Valkanov UCLA First Draft: July 31,
More informationThe Persistence and Predictability of ClosedEnd Fund Discounts
The Persistence and Predictability of ClosedEnd Fund Discounts Burton G. Malkiel Economics Department Princeton University Yexiao Xu School of Management The University of Texas at Dallas This version:
More informationSensex Realized Volatility Index
Sensex Realized Volatility Index Introduction: Volatility modelling has traditionally relied on complex econometric procedures in order to accommodate the inherent latent character of volatility. Realized
More informationWooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares
Wooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares Many economic models involve endogeneity: that is, a theoretical relationship does not fit
More informationIs the Basis of the Stock Index Futures Markets Nonlinear?
University of Wollongong Research Online Applied Statistics Education and Research Collaboration (ASEARC)  Conference Papers Faculty of Engineering and Information Sciences 2011 Is the Basis of the Stock
More informationTable 4. + γ 2 BEAR i
Table 4 Stock Volatility Following Hedge Funds Reported Holdings This table reports the output from crosssectional regressions of future excess volatility against aggregate hedge fund demand for holding
More informationThe Determinants and the Value of Cash Holdings: Evidence. from French firms
The Determinants and the Value of Cash Holdings: Evidence from French firms Khaoula SADDOUR Cahier de recherche n 20066 Abstract: This paper investigates the determinants of the cash holdings of French
More informationReview for Exam 2. Instructions: Please read carefully
Review for Exam 2 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems You are not responsible for any topics that are not covered in the lecture note
More information